where \(\Delta f\)  is sub-carrier spacing and \(\tau = \Vert \mathbf {p}_{\text{tx}}-\mathbf {p}_{\text{ris}}\Vert /c+ \Vert \mathbf {p}_{\text{rx}}-\mathbf {p}_{\text{ris}}\Vert /c\)  for speed of light \(c\) . Finally, \(\mathbf {b}=\mathbf {a}_t \odot \mathbf {a}_r\) , where
the vectors \(\mathbf {a}_t\)  and \(\mathbf {a}_t\)  are the NF array response vectors from the RIS to the TX and RX, respectively. The \(m\) th elements of these vectors are defined as [1]}
\([\mathbf {a}_t]_m = e^{-\jmath \frac{2\pi }{\lambda } \left(R^{t}_{m}-R^{t}_o\right)} ,\) 
\([\mathbf {a}_r]_m = e^{-\jmath \frac{2\pi }{\lambda } \left(R^{r}_{m}-R^{r}_o\right)}, \) 
